We now apply our model to study the behavior of cells in a plane Couette (linear shear) flow setup and compare the steady cell deformation to other numerical and analytical cell models of [1]}, [2]} and [3]}.
A sketch of the simulation setup is shown in figure REF .
For simplicity, we choose \(w=1\)  to reduce the Mooney–Rivlin description (REF ) to two free parameters \(\mu \)  and \(\kappa \)  (or \(E\)  and \(\nu \) ), obtaining a compressible neo-Hookean form.
We use the Lattice Boltzmann implementation of the open source software package ESPResSo [4]}, [5]}.
Coupling between fluid and cell is achieved via the immersed-boundary algorithm [6]}, [3]} which we implemented into ESPResSo [8]}, [9]}.
We note here that, in contrast to [3]}, we do not subtract the fluid stress within the particle interior.
This leads to a small viscous response of the cell material in addition to its elasticity.
To obtain (approximately) the limit of a purely elastic particle, we exploit a recently developed method by [11]} to discriminate between the cell interior and exterior during the simulation.
Using this technique, we can tune the ratio between inner and outer viscosity \( \lambda \)  with \( \lambda \rightarrow 0\)  representing a purely elastic particle.
For simplicity, we will nevertheless set \( \lambda =1\)  in the following, except where otherwise noted.

Details of the method are provided in the SI (section S-4.1).
As measure for the deformation, we investigate the Taylor parameter \(D\)  (REF ) of our initially spherical cell model in shear flow at different shear rates \(\dot{\gamma }\) .
